Unformatted text preview: nt if each can be obtained
from the other by a ﬁnite sequence of row operations.
Rephrase (c) of the theorem:
An n × n matrix A is invertible if and only if A is row equivalent to
In . Outline Elementary Matrix Inverse of an Elementary Matrix The Inverse of a Matrix Finding the Inverse of a Matrix
If A is an invertible n × n matrix, and C = [A | In ], then
rref (C ) = [In | A−1 ].
Er Er −1 · · · E1 A = In , where Ei is the elementary matrix
corresponding to the i th elementary row operation in the
sequence required to obtain In .
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